Upgraded Breaking Of The HLS Model: A Full Solution to the tau-e+e- and phi Decay Issues And Its Consequences On g-2 VMD Estimates

The muon anomalous magnetic moment $a_\mu$ and the hadronic vacuum polarization are examined using data analyzed within the framework of a suitably broken HLS model. The analysis relies on all available scan data samples and leaves provisionally aside the existing ISR data. Our HLS model based global fit approach allows for a better check of consistency between data sets and we investigate how results depend on different strategies which may be followed. Relying on global fit qualities, we find several acceptable solutions leading to ambiguities in the reconstructed value for $(a_\mu)_{th}$. Among these, the most conservative solution is $a_\mu^{\rm had,LO}[{\rm HLS \ improved}]=687.72(4.63) \times 10^{-10}$ and $(a_\mu)_{th}=11\,659\,175.37(5.31)\times 10^{-10}$ corresponding to a $4.1 \sigma$ significance for the difference $\Delta a_\mu=(a_\mu)_{exp}-(a_\mu)_{th}$. It is also shown that the various contributions accessible through the model yield uniformly a factor 2 improvement of their uncertainty. The breaking procedure implemented in the HLS model is an extension of the former procedure based on the BKY mechanism. This yields a quite satisfactory simultaneous description of most $e^+e^-$ annihilation channels up to and including the $\phi$ meson ($\pi^+\pi^-$, $\pi^0\gamma$, $\eta\gamma$, $\pi^+\pi^-\pi^0$, $K^+K^-$, $K^0 \bar{K}^0$) and of a set of 10 (mostly radiative) decay widths of light mesons. It also allows to achieve the proof of consistency between the $e^+e^- \to \pi^+\pi^-$ annihilation and the $\tau^\pm \ra \pi^\pm\pi^0 \nu$ decay and gives a solution to the reported problem concerning the measured partial width ratio $\Gamma(\phi \to K^+K^-)/\Gamma(\phi \to K^0 \bar{K}^0)$. Prospects for improving the VMD based estimates of $a_\mu$ are emphasized.